These notes give a beautiful exposition of the theory of representations of the group ${\rm GL}(2,K)$, where $K$ is a finite field. In 71 well-organized pages, the author manages to cover a remarkable amount of material clearly, concisely, and with many details. The table of contents goes like this:Preliminaries (induced representations of finite groups and the conjugacy classes of ${\rm GL}(2,K)$, etc.); The representations of ${\rm GL}(2,K)$ (inducing representations from the upper triangular subgroup, construction of the cuspidal representations of ${\rm GL}(2)$ via characters of the quadratic extension of $K$, the small Weil group and the small reciprocity law); $\Gamma$-functions and Bessel functions (Whittaker models, computation of $\Gamma$-factors, and computation of the character table for ${\rm GL}(2,K)$).

The reviewer heartily recommends these notes for anyone interested in either entering this research area or teaching a self-contained introduction to the theory of group representations. Although many of the proofs given exploit the fact that $K$ is finite, in presenting the material the author definitely has in mind the current research being done in the theory of (infinite-dimensional) representations of ${\rm GL}(2)$ (and more general groups) over a local (as opposed to a finite) field $K$. -- Stephen Gelbart, Mathematical Reviews